Force field compensation can be learned without proprioceptive error
A Melendez-Calderon 1 , L Masia2 , M Casadio3 and E Burdet1
1 Department
of Bioengineering, Imperial College London, UK; e.burdet@imperial.ac.uk
2 Robotics,
Brain and Cognitive Sciences, Italian Institute of Technology, Italy
3 Department
of Informatics, Systems and Telematics, University of Genova, Italy
Abstract— Robotic devices able to train both reaching and
manipulation, involving multiple degrees-of-freedom (DOF), are
often large and complex. Could mechanically simpler devices
be used to train people, by using only visual feedback and
constraining the limb in one or more of the degrees of freedom
during task performance? This study examines how this motion
guidance influences motor learning in healthy subjects, when
virtual kinematic error is provided as visual feedback. The
results demonstrate that i) virtual learning is possible, though
the learning pattern are slightly different than in learning with
full proprioception error, and ii) the inverse model learned is
similar in the two conditions.
y
x
y
x
I. BACKGROUND OF THE STUDY
Robotic systems have been developed in recent years to
train activities of daily living (ADL), e.g. [1]–[3]. To control
movements in the space, these systems generally involve a
large number of degrees-of-freedom (DOF). For example,
ARMin II [3] has six DOF to enable positioning of the hand
in the 3D workspace and Gentle/S [2] has 9 DOF to train
both reaching and grasping in a reach-grasp-transfer-release
sequence. As a consequence, these systems are often large
and costly, and hardly compatible with a decentralized use.
Is it possible to train functional tasks using compact robotic
devices with limited DOF? To perform arbitrary movements
in the 3D space, humans would need at least 6 DOF, even
more if hand and fingers movements are considered. However,
neuroscience studies have shown that humans generally use
regular motion patterns involving few DOF or synergies [4],
simplifying motion control.
Could we use these motion invariances to simplify the
design of dedicated rehabilitation devices? For example, it is
well known that, in reaching movements, the hand follows
approximately a straight line path from the start to the target
[5]. Therefore, ARM Guide [6] has only one active DOF,
which considerably simplifies the design and makes the device
safer and cheaper relatively to systems moving in 6 DOF.
In a recent study [7], we analyzed typical movements
of healthy subjects in three critical ADL: pick-and-place of
objects, drinking and eating. The results showed that the hand
path remains mainly confined to a vertical plane, and the
deviation relatively to this plane is only 5% of the traveled
distance [7]. Based on these results, one could assume that
lateral deviation is negligible and one could create training
devices on which the hand path is constrained to move in
a channel. The question we investigate here is whether/how
these lateral constraints influence learning, and if providing
Fig. 1. Subject performing horizontal arm movements with/without lateral
constraint using the Braccio di Ferro workstation.
kinematic error is sufficient to promote a reliable feedforward
internal model of a real task.
II. L EARNING A VIRTUAL FORCE FIELD
To address this question we let subjects experience both a
virtual and a real velocity dependent force field (VF) defined
by
0
25
ẋ
Fx
=
,
(1)
Fy
−25 0
ẏ
where the force applied on the hand F is in N and the hand
velocity (ẋ, ẏ)T in m/s. In order to compensate for the lack
of lateral motion error, our idea is to provide visual feedback
of this error, computed from a model of the subject’s arm and
robot’s dynamics.
The paradigm consists in learning the virtual VF while
moving along a channel (of stiffness 4000N/m and damping 100Ns/m) when performing horizontal point-to-point arm
movements. For this purpose we used the Braccio di Ferro
(BDF) manipulandum shown in Fig.1 at the Human Behavior
Lab of the Italian Institute of Technology.
The channel constrains movement to the y axis, hence
proprioceptive feedback on the x deviation is absent, and
the VF is basically virtual (vVF). However, the subjects are
provided with visual feedback of the estimated hand trajectory
as without channel. The simulated trajectory was estimated
using a subject-specific arm model (arm dynamics modeled as
in [8], [9] and anthropometrical data obtained from tables in
O. Dössel and W.C. Schlegel (Eds.): WC 2009, IFMBE Proceedings 25/IX, pp. 381–383, 2009.
www.springerlink.com
382
A. Melendez-Calderon et al.
Robot
Model
Robot
dynamics
-
Lateral force
Subject-robot
j
interaction
Real
kinematics (Y)
After-effects
+
Velocity
dependant
Force field
+
Human
Arm Model
Catch-trials Real VF
Subject 1
Virtual
kinematics (X)
Visual
Display
Before-effects
Subject 2
Subject 3
0.10
VF (X)
0.05
Y [m]
VF (Y)
Fig. 2.
Diagram of dynamic model implementation.
0.00
-0.05
-0.10
Subject 4
•
•
•
•
0.00
-0.05
-0.10
Familiarization: 25 successful movements constrained in
a channel and with no vVF but with feedback of the
estimated hand trajectory. This, in order to familiarize
with the model dynamics without any learning.
Learning: 80 successful movements in a channel and with
a vVF, i.e. feedback of the estimated had trajectory with
a vVF.
Testing real VF: 25 movements on which 20 were performed in a channel with vVF and 5 pseudo-random catch
trials with a rVF.
Testing after-effects: 25 movements on which 20 were
performed in a channel with vVF and 5 pseudo-random
catch trials with no channel and no rVF.
Washout: 25 successful movements with no channel and
no rVF.
Baseline (before-effects): 25 movements on which 20
were performed with no channel and no rVF, and 5
pseudo-random catch trials with rVF.
Subject 7
Subject 8
Subject 9
0.10
0.05
Y [m]
Nine right-handed male subjects, with no history of neurological disease, naive to the device and to the task, were
recruited for this experiment. The task consisted in performing
unidirectional point-to-point movements of amplitude 20cm in
0.6±0.1s with the dominant hand from a 2cm diameter origin
of to a circular target of the same size. Time started from
the moment the subject left the origin and stopped once he
reached the target.
Subjects were instructed to perform the movement as
straight as possible within the specified time range. Feedback
of the trial performance was provided to the subjects indicating
them whether they perform “too slow”, “too fast”, or if their
movement was successful. A trial was successful when the
subject moved the hand from the origin to the target within
the specified time.
Each subject performed five trials in six phases:
•
Subject 6
0.05
III. P ROTOCOL
•
Subject 5
0.10
Y [m]
[10]), a linear second-order robot model, the vVF, the lateral
force applied to the channel and the hand position in the y
direction, as shown in Fig.2.
Once the subjects have trained in the virtual VF, the channel
is removed allowing them to move in the 2D space under a
real VF (rVF) and a real Null Field (rNF). This enables us
to determine whether subjects learned within the limited DOF
conditions, and to observe the after effects of the learning.
0.00
-0.05
-0.10
-0.05
0.00
X [m]
0.05
-0.05
0.00
X [m]
0.05
-0.05
0.00
X [m]
0.05
Fig. 3. Comparison between (red) before-effects, (green) after-effects and
(blue) catch trials of real VF after learning the virtual VF. The thick lines
represent the mean trajectory of each block.
IV. R ESULTS
Catch trials on which the channel was removed and a rVF
was applied to the subjects after having learned the virtual VF
suggest that subjects were able to learn compensating for the
VF in a lateral constrained condition. This is shown by the
trajectory in rVF after having learned in vVF, which is almost
straight as illustrated in Fig.3.
Fig.4 shows the learning phase of a representative subject,
and it can be observed that the learning rate is not as fast
as it would be when learning in normal conditions (e.g. [11]).
Nevertheless, this learning led to a fairly good inverse model of
the real task dynamics as suggested by the catch trials during
the testing phase (Fig.5).
A comparison between the angular aiming error of the last
10 trials of learning phase and the catch trials of rVF of all
subjects showed there was no statistically significant difference (p=0.17) between the virtual and the real environments.
Subjects reported to be unaware of both rVF catch trials and
IFMBE Proceedings Vol. 25
Force Field Compensation Can Be Learned without Proprioceptive Error
383
of being laterally constrained during the learning phase with
vVF.
First 10 trials
0.15
Mean Trajectory
Trials in virtual VF
Too Fast
OK
Too Slow
Middle trials
Too Fast
OK
Too Slow
Catch trials of real VF
0.15
Last 10 trials
0.10
Y [m]
Y [m]
0.10
0.05
0.00
0.00
-0.05
-0.05
-0.10
0.05
-0.05
0.00
0.05
-0.05
0.00
X [m]
0.05
-0.05
X [m]
0.00
-0.10
0.05
-0.05
X [m]
0.00
0.05
-0.05
X [m]
0.00
0.05
X [m]
0.4
0.03
0.02
Y ‘ [m/s]
Mean Square Error [m]
0.5
0.04
0.01
0.00
0
20
40
60
80
100
120
Trial Number
Fig. 4.
0.3
0.2
0.1
0.0
0
Learning session of a representative subject in the virtual VF.
Velocity profiles of the all catch trials in rVF conditions
showed that in some cases there is slight movement correction
at approximately 625ms after initiation of the movement. This
happened in approximately 54.54% of all the experiment catch
trials in rVF conditions. These could be due to inconsistencies
between the model and the real arm-robot dynamics.
We are currently performing complementary experiments
for learning in multiple directions using virtual kinematic error
as well as the effect of retention of learning when providing
kinematic error.
V. ACKNOWLEDGMENT
This work in funded in part by the EU-FP7 grant HUMOUR, IIT and Imperial College. A Melendez doctoral studies are sponsored by CONACYT-Mexico.
R EFERENCES
[1] L. Masia, H. I. Krebs, P. Cappa, and N. Hogan, ”Design and Characterization of Hand Module for Whole-Arm Rehabilitation Following
Stroke,” in IEEE/ASME Transactions on Mechatronics. vol. 12, pp. 399407, 2007
[2] R.C.V. Loureiro and W. S. Harwin,Reach and grasp therapy: Design and
control of a 9-DOF robotic neuro-rehabilitation system, Proc. 10th Int.
Conf. on Rehabilitation Robotics, Noordwijk, The Netherlands, 2007,
pp. 757-763
[3] T. Nef, M. Mihelj, G. Kiefer, C. Perndl, R. Muller and R. Riener,ARMin
Exoskeleteon for arm therapy in stroke patients, Proc. 10th Int. Conf. on
Rehabilitation Robotics, Noordwijk, The Netherlands, 2007, pp. 68-74
[4] N Bernstein The co-ordination and regulation of movements, Pergamon,
London, 1967.
[5] P. Morasso, ”Spatial Control of Arm Movements”, Experimental Brain
Research 42: 223-227, 1981.
20
40 60
Time [cs]
80 100
0
20
40 60
80 100
Time [cs]
Fig. 5. Comparison between trials in virtual VF and catch trials of real VF
of the same subject as in Fig.4 during the testing phase.
[6] L. E. Kahn, W. Z. Rymer, and D. J. Reinkensmeyer, ”Adaptive assistance
for guided force training in chronic stroke,” in Proceedings of the 26th
Annual International Conference of the IEEE Engineering in Medicine
and Biology Society., San Francisco, CA, USA, pp. 2722-2725, 2004.
[7] C.F.Yeong, A. Melendez-Calderon and E. Burdet, ”Analysis of Pick-andplace, Eating and Drinking Movements for the Workspace Definition of
Simple Robotic Devices”, submitted to IEEE International Conference
on Rehabilitation Robotics (ICORR), 2009.
[8] Burdet, E., Tee, K., Mareels, I., MILNER, T.E., Chew, C., Franklin, D.,
Osu, R. and Kawato, M. ”Stability and motor adaptation in human arm
movements”. Biological Cybernetics, 94, 20-32, 2006.
[9] Tee, K. P., Burdet, E., Chew, C.M. and Milner, T.E. ”A model of force
and impedance in human arm movements”. Biological Cybernetics, 90,
368-375, 2004.
[10] Winter, D.A. ”Biomechanics and motor control of human movement”,
John Wiley & Sons, 2004.
[11] Franklin DW, So U, Burdet E, and Kawato M. ”Visual Feedback Is Not
Necessary for the Learning of Novel Dynamics”. PLoS ONE, 2007.
IFMBE Proceedings Vol. 25